In this subsection, we include additional empirical results which focus on the convergence properties of spectral regularization for training DNNs. The first objective we study is in validating whether stochastic gradient descent (SGD) indeed converges to approximate first order stationary interpolators (def:afosi). The goal of these experiments are to see whether, upon running SGD, the MSE loss gets sufficiently small even when the training loss, against which stochastic gradients are computed, is augmented with spectral regularization. In Fig. REF , we plot the empirical training and validation loss of DNNs trained both with the MSE loss and the additional spectral regularization. We use a depth-4 fully connected network (learning rate\(=1\times 10^{-1}\) ) to train on the fluorescence protein [1]} dataset (also used in the main paper).
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